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Boston College

1. Cai, Yuanqing. Theta representations on covering groups.

Degree: PhD, Mathematics, 2017, Boston College

URL: http://dlib.bc.edu/islandora/object/bc-ir:107492

Kazhdan and Patterson constructed generalized theta
representations on covers of general linear groups as
multi-residues of the Borel Eisenstein series. For the double
covers, these representations and their (degenerate-type) unique
models were used by Bump and Ginzburg in the Rankin-Selberg
constructions of the symmetric square L-functions for GL(r). In
this thesis, we study two other types of models that the theta
representations may support. We first discuss semi-Whittaker
models, which generalize the models used in the work of Bump and
Ginzburg. Secondly, we determine the unipotent orbits attached to
theta functions, in the sense of Ginzburg. We also determine the
covers for which these models are unique. We also describe briefly
some applications of these unique models in Rankin-Selberg
integrals for covering groups.
*Advisors/Committee Members: Solomon Friedberg (Thesis advisor).*

Subjects/Keywords: covering group; doubling construction; Fourier coefficient; semi-Whittaker coefficient; Theta representation; unipotent orbit

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Cai, Y. (2017). Theta representations on covering groups. (Doctoral Dissertation). Boston College. Retrieved from http://dlib.bc.edu/islandora/object/bc-ir:107492

Chicago Manual of Style (16^{th} Edition):

Cai, Yuanqing. “Theta representations on covering groups.” 2017. Doctoral Dissertation, Boston College. Accessed August 11, 2020. http://dlib.bc.edu/islandora/object/bc-ir:107492.

MLA Handbook (7^{th} Edition):

Cai, Yuanqing. “Theta representations on covering groups.” 2017. Web. 11 Aug 2020.

Vancouver:

Cai Y. Theta representations on covering groups. [Internet] [Doctoral dissertation]. Boston College; 2017. [cited 2020 Aug 11]. Available from: http://dlib.bc.edu/islandora/object/bc-ir:107492.

Council of Science Editors:

Cai Y. Theta representations on covering groups. [Doctoral Dissertation]. Boston College; 2017. Available from: http://dlib.bc.edu/islandora/object/bc-ir:107492

Boston College

2. Leslie, Spencer. Theta liftings on higher covers of symplectic groups.

Degree: PhD, Mathematics, 2018, Boston College

URL: http://dlib.bc.edu/islandora/object/bc-ir:107937

We study a new lifting of automorphic representations
using the theta representation ϴ on the 4-fold cover of the
symplectic group, \Sp̅_{2r}(\A). This lifting produces
the first examples of CAP representations on higher degree
metaplectic covering groups. Central to our analysis is the
identification of the maximal nilpotent orbit associated to ϴ. We
conjecture a natural extension of Arthur's parameterization of the
discrete spectrum to \Sp̅_{2r}(\A). Assuming this, we
compute the effect of our lift on Arthur parameters and show that
the parameter of a representation in the image of the lift is
non-tempered. We conclude by relating the lifting to the dimension
equation of Ginzburg to predict the first non-trivial lift of a
generic cuspidal representation of
\Sp̅_{2r}(\A).
*Advisors/Committee Members: Solomon Friedberg (Thesis advisor).*

Subjects/Keywords: Arthur parameters; automorphic representations; CAP representations; metaplectic group; theta correspondence

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Leslie, S. (2018). Theta liftings on higher covers of symplectic groups. (Doctoral Dissertation). Boston College. Retrieved from http://dlib.bc.edu/islandora/object/bc-ir:107937

Chicago Manual of Style (16^{th} Edition):

Leslie, Spencer. “Theta liftings on higher covers of symplectic groups.” 2018. Doctoral Dissertation, Boston College. Accessed August 11, 2020. http://dlib.bc.edu/islandora/object/bc-ir:107937.

MLA Handbook (7^{th} Edition):

Leslie, Spencer. “Theta liftings on higher covers of symplectic groups.” 2018. Web. 11 Aug 2020.

Vancouver:

Leslie S. Theta liftings on higher covers of symplectic groups. [Internet] [Doctoral dissertation]. Boston College; 2018. [cited 2020 Aug 11]. Available from: http://dlib.bc.edu/islandora/object/bc-ir:107937.

Council of Science Editors:

Leslie S. Theta liftings on higher covers of symplectic groups. [Doctoral Dissertation]. Boston College; 2018. Available from: http://dlib.bc.edu/islandora/object/bc-ir:107937